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Corrections for Woodwind Tone-Hole Calculations

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The resonance frequencies of a woodwind instrument can be calculated by modelling it as a lattice of series and parallel tube pieces. For greater accuracy, corrections due to local changes in compliance and inertance by the presence of holes must be taken into account. The compliance change due to a closed hole is determined by its volume. The inertance change is dependent on both hole volume and shape. A quick estimate of the inertance is obtained when approximating the flow as stratified and summing the results of the parallel layers using values from accurately obtainable two-dimensional results. This solution has a systematic error. A correct solution is obtained by a finite difference method, but its accuracy is limited by the number of elements which can be handled by a computer. Results of both approaches are compared. For a closed cylindrical hole, the volume contributing to the (negative) inertance change is found to be approximately 28% of the hole radius times its area. The inner end correction for an open hole is found to vary between 82% and 16% of the hole radius when the ratio of hole and tube radii varies between zero and unity.
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Document Type: Research Article

Publication date: September 1, 1998

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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